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Let $(G,\cdot)$ be a locally compact Abelian topological group with Haar measure. It is known that if $B$ is a measurable subset of $G$ of finite and positive Haar measure then $int(B \cdot B)\neq \emptyset$ (Hewitt, Ross, Abstract harmonic analysis I, Cor.20.17 p.296). My question is whether the interior of $B \cdot B$ has to contain square of some element of $G$? Thanks.

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